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Speaker |
Pandya, Aalok |
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| Talk Title |
Curvature and Torsion in Quantum Geometrodynamics |
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Abstract |
Formulation of curvature and torsion in Quantum Geometrodynamics is discussed. Torsion in quantum evolution for symmetric states is found to be: $\tau^2=\frac {\langle H^6\rangle}{\langle H^4\rangle\langle H^2\rangle}$. Curvature in the quantum evolution formulated earlier by Brody and Houghston in terms of moments of Hamiltonian as $\kappa^2=\frac {\langle H^4\rangle}{\langle H^2\rangle^2}-\frac {\langle H^3\rangle^2}{\langle H^2\rangle^3}$ is verified. Thus, the formulation of curvature in quantum evolution is reassuring in more than one ways. The Geometry of $Serret-Frenet$ formulae is recast in the context of Geometric Quantum Mechanics. The Geometry of quantum neighborhood also leads to the formulation of curvature and torsion during quantum evolution. Estimator problem when subjected to neighborhood test brings about many significant results. Fourth order term in the quantum neighborhood test carries information of curvature whereas the sixth order term conveys significant information regarding torsion. Interestingly, expressions of curvature as well as torsion as described in this exercise for Quantum Geometrodynamics are experimentally measurable quantities. |
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